Certain families of straight walled revolver cartridges are reverse compatible, meaning the later, longer cases are a stretched or 'magnumised' version of the earlier shorter cartridge. In these cases the shorter case can be fired in the longer cylinder, the only side effect being the need to clean up the cylinder after shooting as you may get a ring of carbon form on the cylinder wall at the point where the shorter case mouth sits.
The most common example of a stretched case is the .38 Special/.357 Magnum family. The original case was the .38 Short Colt, which was stretched to become the .38 Long Colt, which was stretched to become the .38 Special, which was stretched to become the .357 magnum, which was stretched to become the .357 Maximum.
The .38 special &.357 magnum are the only two members of the family that are common at gun shops and it is normal for shooters to buy .38 specials for target shooting and .357 magnums for self defence, both being fired through the same gun.
In your case the cartridge family started with the .32 S&W, which was stretched to become the .32 S&W long, which was stretched to become the .32 H&R Magnum, which was stretched to become the .327 Federal. Each was more powerful than the earlier cartridge.
Your gun isn't from the top of the power tree, not being chambered for the .327 Federal, but is chambered for a reasonably powerful self defence cartridge, the .32 H&R magnum.
.32 S&W long is no where near as powerful as the .32 H&R Magnum, so it will be easier to shoot in practise and probably cheaper too. The downside is that in a self defence shooting the .32 S&W long may not be powerful enough to stop an attacker.
My advice is you shoot off the .32 S&W long at the range for practise and also buy and shoot at least a few .32 H&R Magnums so you are loaded with and familiar with the better cartridge.
just remember to clean the cylinder chambers well after shooting the longs.
I hope this helps.
